@Einstein
It's home made. I wrote it long time ago, but I remember that for the interpolation, I did not find anything suitable and usable for my level of math in the literature.
For the upsampling of the triangulation, I remember that I tried the Steiner refinement approach, but it did not work well for what I wanted to do. So, I built my own method.
I was not familiar with the butterfly subdivision algorithm and still am not. Maybe it is a more conventional approach.